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A 8000kg engine pulls a train of 5 wagons, each of 2000kg, along a horizontal track. If the engine exerts a force of 40000N and the track offers a friction force of 5000N, then calculate:
(a) The net accelerating force:
(b) The acceleration of the train; and (c) The force of wagon 1 on wagon 2.
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Given : Mass of engine M=8000 kg Mass of each wagon m=2000 kg Frictional force acting in backward direction f=5000 N (a) : The net force acting on the train F ′ =F−f=40000−5000=35000 N
(b) : Let the acceleration of the train be a ∴ F ′ =(5m+M)a 35000=(5×2000+8000)a ⟹a=1.944 ms −2
(c) : External force is applied directly to wagon 1 only. The net force on the last four wagons is equal to the force applied by wagon 2 by wagon 1. Let the acceleration of the wagons be a ′ 35000=(5m)a ′ ⟹35000=10000×a ′ Acceleration of the wagons a ′ =3.5 ms −2 Mass of last 4 wagons m ′ =4×2000 kg ∴ Net force on last 4 wagons F 1 =8000×3.5 =28000 N Thus force on wagon 2 by wagon 1 is 28000 N.
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